Question

Show that 2^[x+1]-2^[x-1]= 15 can be written as 2[2^x]-1/2[2^x]= 15

Answer 1

Explanation:

2^[x+1]-2^[x-1]

=2^x×2-[2^x]÷2

=2[2^x]-1/2[2^x]

so 2^[x+1]-2^[x-1]= 15 can be written as 2[2^x]-1/2[2^x]= 15 !

Answer 2

`~~~~~~2^(x+1) - 2^(x-1) = 15\\\\\implies 2^x \cdot 2^1 - 2^x \cdot 2^(-1)=15~~~~~~~~~~~~~~~~~~;[a^m * a^n = a^(m+n)]\\\\\implies 2 \left(2^x\right) - \frac 12 \left(2^x \right) = 15~~~~~~~~~~~~~~~~~~~~;\left[a^(-n) = \frac 1{a^n},~~~a\\eq 0 \right]\\\\\text{Showed.}`